Speaking from a dressage point of view - college programs for riders are not held in much esteem. What stands up if you decide to be a "horse trainer" is real world riding and competitive experience in international rings. First you must learn to ride before you can expect to teach a horse or rider. If you yourself don't know the progression of training a horse, how can you expect to relay it to a horse or rider? This costs money, takes a lot of lessons and is a big investment into your future in horses.
I am just starting out coaching and riding for money. I myself have international riding experience and have trained my own horses, with the help of coaches, and of course have my own coach to defer to if any of my students or horses run into problems. So far I have been able to work through most of the issues that I have come across in my clients' horses and riding, but I do always encourage my clients to ride with my coach in clinics, or at least audit if it is not in the budget to ride. Even with my experience and the potential client base, it would be impossible for me to sustain myself by riding horses and giving lessons while still competing myself, having a truck and trailer, taking lessons, etc.. And so I have a day job, I organize horse shows and I teach for a small amount of income.
I imagine in 20 years if I am still interested in coaching and riding, at that point I will have experience at a WEG or Olympics and can then charge more, and hopefully sustain myself on lessons and clinics. But without that experience, at $40/45 minutes, there is no way I would be able to support myself without a real job.
Even with a lot of experience and riding internationally and being very good, it is very, very tough to make ends meet as a f/t horse trainer without someone else supporting you.